\chapter{Conclusion}

In this report, we reviewed the current literature on machine learning systems for communcations systems; specifically equalization and carrier frequency offset.  We also discussed the value of robustness and adaptability in future communications systems requiring an investigation of meta-learning.
We demonstrated that neural networks can learn to learn to estimate channel characteristics for two tap channels.  We explored using deep recursive neural networks to learn to learn to equalize.
We also used recursive neural networks to learn to learn to be a clock by rotating in a circle at different rates.  Lastly, we used deep neural networks to estimate the rate of carrier frequency offset and correct it.

All of this was achieved without using backpropagation when faced with new environments.
From here, we plan to continue developing our work and design an end-to-end receiver, including demodulation and error correction, in neural networks that can adapt to new multipath channels and carrier frequency offsets. 
Communications is a perfect application to explore the possibilities and limitations of the current meta-learning and machine learning frameworks.  
